A236514 Primes with a binary weight greater than or equal to the binary weight of their squares.

2, 3, 7, 23, 31, 47, 79, 127, 157, 191, 223, 317, 367, 379, 383, 479, 727, 751, 887, 1087, 1151, 1277, 1279, 1451, 1471, 1531, 1663, 1783, 1789, 1951, 2297, 2557, 2927, 3067, 3259, 3319, 3581, 3583, 3967, 4253, 4349, 5119, 5231, 5503, 5807, 5821, 6079, 6143, 6271, 6653, 6871, 6911, 7039, 7103, 7151

Offset: 1

Author

Irina Gerasimova, Jan 27 2014

Keywords

• nonn
• base

Comments

Primes p such that A000120(p) = A000120(p^2): 2, 3, 7, 31, 79, 127, 157, 317, 379, 751, 1087, 1151, 1277, 1279,...

Examples

			2 is in this sequence because 2 is 10 in binary representation, and it has as many 1s as its square 4, which is 100 in binary.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A077436, A094694.

Programs

Mathematica

bc[n_] := DigitCount[n, 2][[1]]; Select[Range[7151], PrimeQ[#] && bc[#] >= bc[#^2] &] (* Giovanni Resta, Jan 28 2014 *)
Select[Prime[Range[1000]], DigitCount[#, 2, 1] >= DigitCount[#^2, 2, 1] &] (* Alonso del Arte, Jan 28 2014 *)

PARI

is(n)=hammingweight(n^2)<=hammingweight(n) && isprime(n) \\ Charles R Greathouse IV, Mar 18 2014

Formula

Primes p such that A000120(p) >= A000120(p^2).